Probability and Statistics for Engineers is written for undergraduate students of engineering and physical sciences. Besides the students of B.E. and B.Tech., those pursuing MCA and MCS can also find the book useful. The book is equally useful to six sigma practitioners in industries.

A comprehensive yet concise, the text is well-organized in 15 chapters that can be covered in a one-semester course in probability and statistics. Designed to meet the requirement of engineering students, the text covers all important topics, emphasizing basic engineering and science applications.

Assuming the knowledge of elementary calculus, all solved examples are real-time, well-chosen, self-explanatory and graphically illustrated that help students understand the concepts of each topic. Exercise problems and MCQs are given with answers. This will help students well prepare for their exams.

Key Features

Discusses all important topics in 15 well-organized chapters.

Highlights a set of learning goals in the beginning of all chapters.

Substantiate all theories with solved examples to understand the topics.

Provides vast collections of problems and MCQs based on exam papers.

Lists all important formulas and definitions in tables in chapter summaries.

Explains Process Capability and Six Sigma metrics coupled with Statistical Quality Control in a full dedicated chapter.

Presents all important statistical tables in 7 appendixes.

Includes excellent pedagogy:

– 177 figures

– 69 tables

– 210 solved examples

– 248 problem with answers

– 164 MCQs with answers

About the author

DR. J. RAVICHANDRAN, Ph.D., is an associate professor at the Department of Mathematics, Amrita Vishwa Vidhyapeetham, Coimbatore, India. Earlier, he served the Statistical Quality Control department at a manufacturing industry for more than 12 years. His areas of research include statistical quality control, statistical inference, six sigma, total quality management and statistical pattern recognition. A senior member of the American Society for Quality (ASQ) for over 20 years and a member of the Indian Society for Technical Education (ISTE), Dr. Ravichandran has contributed to quality higher education by organizing a national-level conference on Quality Improvement Concepts and Their Implementation in higher education and publishing proceedings.

Table of Contents

Preface

1. Probability Concepts

1.1 Introduction

1.2 Important Definitions

1.2.1 Random Experiment

1.2.2 Trial

1.2.3 Sample Space

1.2.4 Mutually Exclusive Events

1.2.5 Independent Events

1.2.6 Dependent Events

1.2.7 Equally Likely Events

1.2.8 Exhaustive Events

1.3 Approaches of Measuring Probability

1.3.1 Mathematical (or Classical or Apriori) Probability

1.3.2 Statistical (or Empirical or Posteriori) Probability

1.3.3 Axiomatic Approach to Probability

1.3.4 Law of Addition of Probabilities

1.3.5 Law of Multiplication of Probability and Conditional Probability

1.4 Bayes’ Theorem

Solved Examples

Summary

Problems

Multiple-Choice Questions

2. Random Variables and Distribution Functions

2.1 Introduction

2.2 Random Variable

2.3 Discrete Random Variable

2.4 Continuous Random Variable

2.5 Cumulative Distribution Function

Solved Examples

Summary

Problems

Multiple-Choice Questions

3. Expectation and Moment-Generating Function

3.1 Introduction

3.2 Definition and Properties of Expectation

3.3 Moments and Moment-Generating Function

3.3.1 Raw and Central Moments

3.3.2 Relationship between Central and Raw Moments

3.3.3 Moments about an Arbitrary Value

3.3.4 Moment-Generating Function

3.3.5 Properties of Moment-Generating Function

3.3.6 Characteristic Function

Solved Examples

Summary

Problems

Multiple-Choice Questions

4. Standard Discrete Distribution Functions

4.1 Introduction

4.2 Discrete Distributions

4.2.1 Binomial Random Variable and Its Distribution

4.2.2 Poisson Random Variable and Its Distribution

4.2.3 Geometric Random Variables and Their Distributions:

4.2.4 Uniform Random Variable and Its Distribution

Solved Examples

Summary

Problems

Multiple-Choice Questions

5. Some Standard Continuous Distribution Functions

5.1 Introduction

5.2 Uniform Random Variable and Its Distribution

5.3 Exponential Random Variable and its Distribution

5.3.1 Definition 1: If λ is given as a number of occurrences per unit time

5.3.2 Definition 1: If λ is given as time per occurrence

5.3.3 Derivation of Mean and Variance using Moment-Generating Function

5.3.4 Memory-less Property of Exponential Distribution

5.4 Gamma Random Variable and Its Distribution

5.4.1 Definition 1: Gamma Distribution with Two Parameters α and β

5.4.2 Definition 2: Gamma Distribution with One Parameter α

5.4.3 Derivation of Mean and Variance using Moment-Generating Function

5.4.4 Some Particular Cases of Gamma Distribution

5.5 Normal Random Variable and Its Distribution

5.5.1 Mean and Variance

5.5.2 Properties of Normal Distribution

5.5.3 Standard Normal Density and Distribution

5.5.4 Derivation of Mean and Variance using Moment-Generating Function